The circulation of blood is fundamental to sustaining life, as it ensures the transport of oxygen and essential nutrients to various parts of the body while also facilitating the elimination of metabolic waste and transmitting chemical signals to the kidneys for processing [1]. Within the circulatory system, the heart's pumping action generates a pulsatile pressure gradient, which propels blood through the vascular network, a phenomenon commonly observed in the pressure pulse measured at the wrist by medical professionals [2]. Additionally, blood serves as a medium for drug transport to tumor cell membranes, where it triggers chemical interactions between tumors and circulating fluids. Optimizing these biological interactions is crucial for enhancing therapeutic treatments [3]. Despite its critical functions, the circulatory system remains a major area of concern due to the high mortality rates associated with cardiovascular diseases. Although medical advancements such as surgery, radiotherapy, chemotherapy, and immunotherapy offer treatment options, a significant gap persists between their effectiveness and patient survival rates [4]. Blood flow dynamics are inherently complex and play a vital role in various physiological processes. Understanding these dynamics is essential for tackling health challenges, particularly in improving drug delivery systems for cardiovascular disease treatment [5]. The study of blood flow under magnetic and electric field influences has gained significant traction due to its implications in medical and physiological applications. Previous research contribution in [6] have emphasized the importance of this field in advancing medical science. Building on these insights, the present study aims to investigate a new approach by applying a fractional non-Newtonian model to magnetohydrodynamic (MHD) blood flow in permeable bifurcated arteries [7]. This approach is motivated by the recognition of blood as a magnetic fluid, as highlighted in previous studies [8].

Recognizing the magnetic properties of blood, this study seeks to expand our understanding of its behavior in MHD flow by incorporating fractional non-Newtonian fluid dynamics, magnetic nanoparticles, and arterial permeability. This innovative approach aims to unravel the intricate relationship between blood's viscoelastic nature, magnetic effects, and the complex geometry of bifurcated arteries. By employing a fractional non-Newtonian fluid model, this research intends to make a significant contribution to the field, offering valuable insights into optimizing medical treatments, particularly in targeted drug delivery and other biomedical applications.